Possibly the most famous self-adjoint operator is the quantum Hamiltonian, \(\hat{H}\)  [1]}.
In quantum mechanics, physical quantities of interest, such as position, momentum, energy, and spin, are represented
by self-adjoint linear operators called `observables', of which one example is the Hamiltonian.
The Hamiltonian describes the evolution of the probabilistic wave function via the time-dependent Schrödinger equation:
\(i\hbar {\frac{d}{dt}}\vert \Psi (t)\rangle ={\hat{H}}\vert \Psi (t)\rangle .\) 
